To begin with, you are competing with up to about 300 other applicants.
They're from all generations. The new graduate from law school, who couldn't land a position practicing law, is going after the same paralegal job you are. And probably that JD is willing and able to accept less compensation than you are.
But, the biggest nut to crack is in how you create that cover letter. Everything in the business world keeps changing. That includes the expectations of those who can offer us work.
Increasingly those receiving our cover letters want us to position and package ourselves with the brilliant controlled creativity of Don Draper from "Mad Men." Instead of straight exposition, the kind we learned in Freshman Composition in college, they want the well-put-together persuasiveness of copywriting. In a sense, our resume has become advertising - for ourselves. It can't be amateurish.
How to become Don Draper 2.0? Analyze all kinds of promotional material. Figure out what seems to be effective and why. On the Internet are billions of articles on how to present whatever in a way that gets the right kind of attention. Should you take a course in marketing communications? That could be a great investment in a tool you can use in myriad ways, beyond your job search.
However, that is just part of the job. Simultaneously, employers demand that we understand business rhetoric. We have to use the appropriate structure, concepts, and word choice to present the edge we are offering and the rest of the experience, skills, and accomplishments necessary to get the job done - better than others competing for that work. Call it "Mad Men Meets Harvard Law School."
To be up-to-date on business protocol in presenting yourself read career guides such as "What Color Is Your Parachute?" Every library has multiple copies. Surf the Internet for articles on the how-to of cover letters to pitch in business. Amazon.com also sells used books on the topic. Make sure the used book you are ordering has been published recently. The guidance has to be geared for the current labor market, which is glutted in many fields.
As you start out experimenting with doing your cover letters as marketing materials, not dry corporatese, know there is a learning curve. The burden is on you to learn. Many of the lessons will come from rejection.